Archive for June, 2015

Problem 809

Find the percentage rate of change of f(x) at the indicated value of x.

f(x) = 10500 – 3x2 ; x = 55

 

Solution:-

 

The percentage rate of change of f(x) at x = 55 is -23.2%

 

Problem 808

Find the equation of the line tangent to the graph of f at the indicated value of x.

f(x) = 16ex + 15x; x = 0

 

Solution:-

 

y =  31x + 16

 

Problem 807

A famous painting was sold in 1945 for $21900. In 1980 the painting was sold for $32.9 million. What rate of interest compounded continuously did this investment earn?

 

Solution:-

 

As an investment,  the painting earned an interest rate of 20.9%.

 

Problem 806

Find all horizontal and vertical asymptotes.

f(x)=\frac{3x^{2}-16x+15}{x^{2}-2x-15}

 

Solution:-

 

The horizontal asymptote(s) is/are  y = 3.

The vertical asymptote(s) is/are = x = -3.

 

Problem 805

 

A manufacturer of hospital supplies has a uniform annual demand for 500000 boxes of bandages. It costs $10 to store one box of bandages for one year and $250 to set up the plant for production. How many times a year should the company produce boxes of bandages in order to minimize the total storage and setup costs?

 

Solution:-

 

The company should produces boxes of bandages 100 times(s) a year.

 

 

Problem 804

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72000 + 40x and p(x) = 300 – x/20 ,0≤x≤6000.

A)    Find the maximum revenue.

B)    Find the maximum profit, the production level that will realize the maximum profit, and the prices the company should charge for each television set.

C)    If the government decides to tax the company $4 for each set it produces, how many seta should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?

 

Solution:-

 

A)    The maximum revenue is $450000.

B)    The maximum profit is $266000 when 2600 sets  are manufactured and sold for $ 170 each.

C)    When each set is taxed at $4, the maximum profit is $255680 when 2560 set are manufactured and sold for $172 each.

 

Problem 803

A deli sells 640 sandwiches per day at a price of $8 each.

A)    A market survey should that for every $0.10 reduction in the price, 20 more sandwiches will be sold. How much should the deli charge in order to maximize revenue?

B)    A different market survey shows that for every $0.20 reduction in the original $8 price, 10 more sandwiches will be sold. Now how should the deli charge in order to maximize revenue?

 

Solution:-

 

A)    The deli should charge $5.6 for a sandwich to maximize revenue.

B)    Now the deli should charge $8 for a sandwich to maximize revenue.

 

Problem 802

A laboratory uses 600 white mice each year for experimental purposes. It costs $6 to feed a mouse for one year. Each time mice are ordered, there is a service charge of $18  for processing the order. How many mice should be ordered each time to minimize the total cost of feeding the mice and placing orders for the mice.

 

Solution:-

 

The laboratory should order 60 mice per order.

 

 

Problem 801

 

A  publishing company sells 900,000 copies of certain books each year. It costs the company $1 to store each book for a year. Each time it must print additional copies, it costs the company $500 to set up the presses. How  many books should the company produce during each printing in order to minimize its total storage and setup costs?

 

Solution:-

 

The company should produce 30,000 books each printing in order to minimize costs.

 

 

Problem 800

Find the probability of correctly answering the first 4 questions on a multiple choice test if random guesses are made and each question has 3 possible answers.

 

Solution:-

 

\frac{1}{81}